Could LMB be made to box-select when used outside of a model, but circle-select when initiated over the mesh?
'Box select on LMB'

Try setting this in User Input: 3D View --> Border Select --> Tweak, Left, Any



(Let me know if you made progress on the SHIFT-drag to add to selection, I am looking for that as well.)

EDIT: I discovered a partial answer. Add a new shortcut, use the same one (type in view3d.select_border) This time check "Extend" and "Shift." Now Box selecting with shift will add to the selection in object and edit modes. 

However there still isn't a way to subtract from the selection that I've found yet. And I don't know how to unmap CTRL-select for adding to selection. Keep me posted if you find a way.